Chemometric Evaluation of Repeatability Using the Autocorrelation Method in High-Performance Liquid Chromatography with Ultraviolet Detection.

The mixed random processes of the first order autoregressive process (AR(1)) and white noise have been proved to provide a good approximation of baseline noise in a variety of analytical instruments, and may therefore be useful for estimating precision profiles. This study aims to examine a recently proposed autocorrelation method for estimating three noise parameters involved in the mixed processes (two for AR(1) and one for white noise) of HPLC, which can then be used to calculate the precision profile. This chemometric method was applied to repeatability evaluations of estriol determination using HPLC with UV detection (HPLC-UV). The relative standard deviations (RSDs) of peak area measurements for 5.0 mg/L estriol were observed to be 1.42% for the autocorrelation method and 1.63% for actual repeated measurements of real samples (n = 6). The theoretical RSDs of the autocorrelation method fell within the 95% confidence intervals of the repeated measurements. It is found that the noise parameters are obtained from real chromatographic baseline via the autocorrelation method. Moreover, the instrumental detection limit of estriol based on ISO 11843 was obtained from the precision profile (plot of RSD of measurements against concentration). This is the first paper to describe the autocorrelation method is a practically useful technique for evaluating the precision profile of HPLC-UV analyses without recourse to the repeated measurements of real samples.

Assessment of Repeatability in Supercritical Fluid Chromatography with Electrochemical Detection Based on the ISO 11843 Part 7.

The present study proposes a method for the assessment of repeatability in supercritical fluid chromatography with electrochemical detection (SFC-ECD), based on the ISO 11843 part 7 (ISO 11843-7:2018) which can theoretically provide detection limits and standard deviation (S.D.) through the stochastic properties of baseline noise without repetitive measurements of real samples. On the baseline noise of SFC-ECD, large-amplitude and periodic noises with less than 0.05 Hz were observed, and the power spectrum of the baseline noise showed 1/f fluctuation (f = frequency). It was found that the present power spectrum analysis, according to the law of error propagation, can provide suitable noise parameters to calculate S.D. of baseline noise and a relative S.D. (RSD) of peak area by ISO 11843-7. The chromatographic determinations of α-, ß-, γ- and δ-tocopherol have been taken as examples. In the present SFC-ECD, the RSDs of peak areas for α-, ß-, γ- and δ-tocopherol obtained by ISO 11843-7 were within 95% confidence intervals of the RSD of them obtained by repetitive measurements (n = 6). Thus, we found that ISO 11843-7 is applicable to the assessment of repeatability in SFC-ECD for determining tocopherols without repetitive measurements.

Effects of digital processing on repeatability assessment of a multiple reaction monitoring liquid chromatography-tandem mass spectrometry system by ISO 11843-7.

ISO 11843 part 7 (ISO 11843-7) can provide a standard deviation (SD) of area measurements of a target peak through the stochastic behaviors of instrumental noises. The purpose of this study is to demonstrate that ISO 11843-7 can be applied to assess repeatability in an isocratic liquid chromatography-tandem mass spectrometry (LC-MS/MS) system without repetitive measurements. The relative standard deviation (RSD) of the peak area of ergosterol picolinyl ester, which was used as an example, on a multiple reaction monitoring (MRM) chromatogram was determined by ISO 11843-7. The RSD by ISO 11843-7 (N = 1) was within a 95% confidence band of the RSD by repetitive measurements (N = 6). Moreover, the effects of digital smoothing, such as moving average, were also examined on the repeatability assessment in LC-MS/MS by ISO 11843-7. From the results of the comparisons of the RSDs obtained by ISO 11843-7 and the repetitive measurements, it was shown that suitable RSDs of the peak area were obtained from the smoothed MRM chromatograms by the moving average for narrow data point windows (e.g., one-sixth of the peak width). In conclusion, the utility of repeatability assessment based on ISO 11843-7 has been expanded for the validation of an LC-MS/MS system.

Chemometric evaluations of repeatability and detection limit in high-performance liquid chromatography with electrochemical detection.

The function of mutual information (FUMI) theory proposes that it is possible to obtain a relative standard deviation (RSD) of the peak area of an analyte from baseline noises and a signal on a single chromatogram when the analyte concentrations are proportional to their peak areas. In this study, we demonstrate that the FUMI theory using noise parametrization by the difference method is applicable for the evaluations of repeatability and detection limit (DL) in high-performance liquid chromatography with electrochemical detection (HPLC-ECD). HPLC-ECD for determining vincristine (VCR) was taken as an example, and VCR was detected on a glassy carbon surface at +0.8 V vs. Ag/AgCl. In the comparisons of precision profiles (plots of RSD of peak area against concentrations of an analyte), the stochastically estimated RSD (N = 1) by the FUMI theory fell within the 95% confidence intervals of statistically estimated RSD (N = 6) by repetitive measurements. Furthermore, the DL obtained by the FUMI theory (3.3×SD) was almost the same value as that by the signal-to-noise ratio (S/N) = 3. Moreover, we introduced a manual method for signal-noise resolution to obtain noise parameters from a chromatogram with low-pass Bessel filter processing. In conclusion, our results show that the FUMI theory using noise parametrization by the difference method can be applied to the evaluations of repeatability and DL in HPLC-ECD without and with a low-pass Bessel filter.

Effects of sampling rate and noise filter processing on repeatability assessment in UHPLC with ultraviolet detection based on the ISO 11843-7.

The present study examines whether short measurement time and noise filter processing in an ultra-high-performance liquid chromatography with ultraviolet detection (UHPLC-UV) contribute to limitations for repeatability assessment based on the ISO 11843 part 7 (ISO 11843-7), which can stochastically provide a measurement standard deviation (SD) caused by baseline noise (SB). In this study, ergosterol was used as an example in UHPLC-UV analysis. From the results of power spectrum analysis of baseline noise, 1024 consecutive digital data points provided a suitable SB. Thus, it was found that an SB can be obtained from about 1 min of baseline when a chromatogram was recorded at sampling rate of 20 points s-1 in the present UHPLC-UV system. The relative SDs (RSDs) of the peak area obtained by the ISO 11843-7 were within 95% of the confidential intervals of the RSDs obtained by repetitive measurements, indicating the ISO 11843-7 is applicable to estimate repeatability in a UHPLC-UV system. In a similar way, we found that the RSD of the peak area obtained from a chromatogram with noise filter processing in UHPLC-UV could also be estimated by the ISO 11843-7. In conclusion, we experimentally demonstrate that short measurement time and noise filter processing are not limitations for repeatability assessment based on the ISO 11843-7.

Chemometric evaluation of repeatability of internal standard methods in high-performance liquid chromatography with a Japanese pharmacopoeia assay for indomethacin as an example.

The purpose of this study is to elucidate uncertainty structures of internal standard (IS) methods as compared with absolute calibration methods in liquid chromatography. A quantitative test of indomethacin with butyl 4-hydroxybenzoate as an IS in high-performance liquid chromatography with ultra-violet detection is taken here as an example. The repeatability is evaluated by both a usual statistical method of repetition and a theoretical approach, called the function of mutual information (FUMI) theory. The latter predicts the precision from noise and signals of instrumental output. Plots of relative standard deviations (RSDs) of measurements against analyte amounts, called precision profiles, are compared between the IS methods for indomethacin and their corresponding absolute calibration methods over a wide range of amount. Sample injection errors are observed to be effectively eliminated at high amounts by the IS methods, but at low amounts where background random noise dominates over the other error, the superiority of the IS methods is overshadowed and the precision of both the methods is almost comparable. The smallest possible amount of IS material without spoiling the integrity of analysis is estimated from the precision profiles.

A simple method for daily inspections of gas chromatography-mass spectrometry systems with an instrumental detection limit as an indicator.

The purpose of this paper is to propose a simple method for daily inspections of a gas chromatography-mass spectrometry (GC-MS) system with an instrumental detection limit (IDL) as an indicator. A definition of DLs by ISO is 3.3σ where σ denotes the standard deviation (SD) of blank measurements. Estimation of σ is carried out according to the function of mutual information (FUMI) theory and actually with commercial software (TOCO19). An IDL which is a combination of a signal area, width and noise level is concluded to be a good indicator for daily inspections compared with each of its constituents. Methyl stearate is used as a standard material for the daily inspection of a programmed-temperature GC-MS system. A short chromatogram of 1800 data points (1.5 min) containing a target signal and background noise is fit for the IDL prediction by TOCO19. The relative SDs (RSDs) based on the theoretically estimated σ are shown to coincide with statistical results from repeated measurements within 95% confidence intervals. Column temperature is observed to affect IDLs through background fluctuation and then temperature-IDL relationship is examined in a range from 170 to 270 °C. Actual daily inspections over a month are demonstrated.

An automated system for predicting detection limit and precision profile from a chromatogram.

This paper presents a basic model of an automated system for predicting the detection limit and precision profile (plot of relative standard deviation (RSD) of measurements against concentration) in chromatography. The fundamental assumption is that the major source of response errors at low sample concentrations is background noise and at high concentrations, it is the volumes injected into an HPLC system by a sample injector. The noise is approximated by the mixed random processes of the first order autoregressive process AR(1) and white noise. The research procedures are: (1) the description of the standard deviation (SD) of measurements in terms of the parameters of the mixed random processes; (2) the algorithm for the parameter estimation of the mixed processes from actual background noise; (3) the mathematical distinction between noise and signal in a chromatogram. When compounds are chromatographically separated, each obtained signal is given the detection limit and precision profile on laboratory-made software. A file of a chromatogram is the only requirement for the theoretical prediction of measurement uncertainty and therefore the repeated measurements of real samples can be dispensed with. The theoretically predicted RSDs are verified by comparing them with the statistical RSDs obtained by repeated measurements. Signal shapes on noise are illustrated at the detection limit and quantitation limit, the signal-to-noise ratios of which are close to the widely adopted values, 3 and 10, respectively.

An automated assessment system of limits of detection and quantitation in gradient high-performance liquid chromatography with ultraviolet detection.

A previous paper of this series of study put forward a basic model of an automated system for predicting detection limits and showed its application to a simple example of isocratic high-performance liquid chromatography (HPLC). This paper describes an expansion of the basic system into gradient HPLC. The most serious problem with the expansion is a long-term variation in backgrounds, called gradient baseline drifts, which in theory cannot be covered by a noise model (stationary random process) of the original system. This paper demonstrates that the above problem can be solved with modifying a parametrization procedure of the noise model. The essential role of the system is to predict the standard deviation (SD) of measurements at low concentrations from a chromatogram without repeated measurements of real samples. Laboratory-made software enables the automated assessment of the limits of detection and quantitation for each of chromatographically separated signals in a single run. Simulated background noise which consists of the stationary noise model with linear slopes is used to confirm the accuracy and reproducibility of the automated prediction. A gradient HPLC determination for cefaclor is taken as an example. The parametrization modification improves the correlation coefficient, r2, between the observed and theoretical distributions of the area measurements from 0.373 to 0.966. The statistical confidence levels of the theoretically predicted relative SDs for cefaclor were verified by comparing them with those obtained by repeated experiments (r2 = 0.989). The limits of detection (= 3.3 × SD = 18.0 µg/L) and quantitation (= 10 × SD = 54.7 µg/L) for cefaclor have signal-to-noise ratios close to the commonly adopted values, 3 and 10, respectively.

Detection limit of measurement of pharmaceuticals labeled with short-lived isotopes in HPLC with flow-through gamma-counter.

This paper proposes a method for estimating the detection limit, which is defined as 3.3 times the standard deviation (S.D.) of blank measurements under the situations where the repetition of measurement is difficult or impossible because of a short half-life of radioactivity. The FUMI theory, which can estimate an S.D. value without repetition in various instrumental analyses, is adopted and proved here to be available in a radio-HPLC system as well. (99m)Tc-ECD (T(1/2)=360.6 min) that is a lipophilic compound for the diagnosis of regional brain perfusion is taken as an example.

Optimization of capillary liquid chromatography with electrochemical detection for determining femtogram levels of baicalin and baicalein on the basis of the FUMI theory.

Capillary liquid chromatography with electrochemical detection (CLC-ECD) was developed for determining the femtogram levels of baicalin and baicalein. The CLC-ECD system and the experimental conditions were optimized based on the precision (=information content) phi and efficiency (=information content/time) theta, which were calculated from a relative standard deviation (R.S.D.) by a chemometric tool called the FUMI theory. When CLC-ECD was established using a capillary column (Inertsil ODS-3, 150 mm x 0.2 mm i.d.), a sample injector fitted with a 0.2 microL injection loop, an applied potential of +650 mV vs. Ag/AgCl, and a flow rate at 1.8 microL/min, baicalin and baicalein were determined at femtogram levels. Moreover, the present method was validated using a chemometric tool and a conventional method. Since the FUMI theory makes it possible to predict R.S.D. without repetitive measurements, the chemometric tool saves considerable amounts of chemicals and experimental time, and was found to be useful for the optimization of conditions and validation for determination by CLC-ECD. The present method was applied to the analysis of Japanese Pharmacopoeia Scutellaria Root and Scutellaria baicalensis Georgi for determining baicalin and baicalein.

Simulation model for predicting limit of detection and range of quantitation of competitive enzyme-linked immunosorbent assay.

The limit of detection (LOD) and range of quantitation (ROQ) of competitive enzyme-linked immunosorbent assay (ELISA) were determined from a model describing the calibration curve and precision profile of the assay. The calibration curve is given by solving the differential equations describing the change in the concentrations of an antigen-antibody complex and an enzyme-conjugated antigen-antibody complex by a Runge-Kutta method. The precision profile is described in terms of possible error sources such as the pipetting volumes of the analyte, enzyme-conjugated antigen, antibody and substrate solutions, calibration curve and inherent absorbances between the wells in an ELISA plate. An appropriate concentration of the enzyme-conjugated antigen that balances a low detection limit and sufficient color development was found to be in a narrow range, which is consistent with the empirical rule. The optimum conditions for competitive ELISA using an antibody with a kinetic property can be designed from our model.

Validation of a method for predicting the precision, limit of detection and range of quantitation in competitive ELISA.

The mathematical model for predicting the precision, limit of detection (LOD) and range of quantitation (ROQ) in a competitive enzyme-linked immunosorbent assay (ELISA) proposed by Hayashi et al. (Anal. Chem., 2004, 76, 1295) was validated. The model describes the relative standard deviation (RSD) of concentration estimates by the RSDs of pipetting volumes of analyte, enzyme-conjugated antigen, antibody and substrate solutions, and the standard deviation (SD) of inherent absorbances between the wells in an ELISA plate. For 6 kinds of direct competitive ELISA kits, the LOD and ROQ predicted by the model agreed well with those obtained by experiments with real samples. It was also confirmed that the model is applicable to the prediction of uncertainty that depends on the pipetting error of the viscous antiserum solution. The model was demonstrated to be useful for estimating the LOD and ROQ of competitive ELISA.

Baseline noise and measurement uncertainty in liquid chromatography.

The stochastic properties of baseline noise in HPLC systems with a UV photo-diode array, photo-multiplier and gamma-ray detector were examined by dividing the noise into auto-correlated random process (Markov process) and an independent process (white noise). The present work focused on the effect of the stochastic noise properties on a theoretical estimation of the standard deviation (SD) of area measurements in instrumental analyses. An estimation theory, called FUMI theory (Function of Mutual Information), was taken as an example. A computer simulation of noise was also used. It was shown that the reliability (confidence intervals) of theoretical SD estimates mainly depends on the following factors: the ratio of the white noise and Markov process occurring in the baselines; the number of data points used for the estimation; the width of a target peak for which the SD is estimated.

Prediction of measurement uncertainty in isotope dilution gas chromatography/mass spectrometry.

An equation is theoretically derived which describes the relative standard deviation (RSD) of the amount ratios of analyte to its isotope-labeled variant in gas chromatography/mass spectrometry (GC/MS) using the stable isotope dilution method. The determination of methyltestosterone is taken as an example. The uncertainty equation proposed is justified by comparing the theoretical RSD values with the experimental RSD values obtained by replication over a wide range of analyte amount. The detection limit and quantitation limit are estimated from the continuous plot (precision profile) of the theoretical RSD against analyte amount.

An expression of uncertainty in calibration using stepwise or separate dilution of a stock solution.

The traditional method for linear calibration can estimate the confidence intervals of calibration lines from a set of experimental data for a single calibration line. However, the following situations, often encountered in laboratories, are out of reach of the method, since the concentrations of the standard solutions are not independent of each other: (A) a standard solution is diluted from a more concentrated one in a stepwise way (stepwise dilution); (B) every standard solution for a calibration experiment is prepared from a stock solution, but the stock solution is newly prepared for each calibration (separate dilution with the variable concentration of the stock solution). This paper puts forward a theory to calculate the confidence intervals of calibration lines in the above situations. Analyses made up of sample weighing, dilution, HPLC measurement and calibration with the linear least-squares fitting are taken as examples. The proposed theory is numerically compared to the traditional method.

Method for estimating infection route and speed of influenza.

This paper puts forward a method for estimating the infection route and speed of influenza from the daily variations in the amount of influenza formulations supplied at distant city pharmacies. The cross-correlation function between the time variations at the pharmacies indicates as for the drug sales, how many days a pharmacy lags behind another pharmacy. The comparison of the time lags between the pharmacies can lead to the estimation of the infection route of influenza. Taking into account the distance between the locations of the pharmacies, we can calculate the infection speed of influenza. Three pharmacies located in Tokyo and its vicinity (Saitama and Kanagawa) are taken as an example. The thrust of this paper is to introduce the new strategy that can take full advantage of the information every pharmacy has in possession.

Method for estimating the order of influenza infection between adults and children.

This paper puts forward a method for determining the infection order of influenza between adults and children from the daily variations in the amount of influenza anti-viral agents treated at a pharmacy. The time series of Tamiflu Capsule for adults and Tamiflu Dry Syrup for children are compared by means of the cross-correlation function. The results from pharmacies located in Tokyo and Kanagawa show that the influenza infection period of adults is earlier than that of children, indicating the infection order: first adults and second children. However, a pharmacy in Saitama yields no clear result.

Method for detecting health injury from prescriptions at a pharmacy.

A method is proposed to detect the abnormal situations of people's health in case of the unexpected outbreak of a disease by monitoring the daily variations in the prescriptions at a pharmacy. The abnormal situations are defined as the situations which are not included in the majority (99.9%) of the normal situations. An epidemic probably caused by infectious micro-organisms in a terrorist attack is taken as an example. The drugs for the typical symptoms are monitored: influenza anti-viral agent and common cold drug. This paper demonstrates that the border between the normal and abnormal situations corresponds to the detection limit which is a fundamental concept in analytical chemistry.

[Birth and death process of computer viruses].

The daily variations in the number of computer viruses found attaching to e-mails and the number of accesses to the home page of a national institute in Japan are examined. The power spectral densities (PSD) of the variation in the computer viruses show a time-correlation characteristic of Markov process, but the daily access number does not (identified as white noise). Like biological viruses, the variation in the computer viruses can be described by the birth-and-death model known as a Markov process.